Worksheet: Grouped Frequency Tables

In this worksheet, we will practice reading and interpreting frequency tables and tally charts and forming a frequency table for a given quantitative data set.

Q1:

The table shows the marks out of 10 that students scored in a test. How many students scored higher than the modal mark?

Mark5678910
Frequency311812105

Q2:

The tally chart shows the marks that students in a class received in a mathematics test. Using the information from the tally chart, complete the frequency table.

Sets5–10–15–20–25–
Tally
Sets5–10–15–20–25–
Frequency
  • A10,14,12,16,6
  • B9,14,12,16,6
  • C9,15,12,16,6
  • D8,13,11,15,5
  • E9,14,12,15,6

Q3:

The table shows the number of classes of varying sizes in a school. Using the data, complete the frequency table.

Class Size161718192021
Number of Classes423514
Class Size16-1718-1920-21
Frequency
  • A9, 9, 10
  • B9, 8, 5
  • C6, 8, 5
  • D6, 5, 9

Q4:

The table shows the marks of 100 students in a recent science exam. How many students received 40 marks or more?

Mark0–910–1920–2930–3940–4950–Total
Frequency61512262318100

Q5:

The frequency table below shows the weights of 40 students in a class. How many students weigh less than 50 kg?

Weight, 𝑤30–35–40–45–50–Total
Frequency58129640

Q6:

The table shows the heights of 100 students in a school. How many students’ heights are greater than or equal to 120 cm?

Height (cm)115–119120–124125–129130–134135–139140–144145–Total
Number of Students12122016121018100

Q7:

The table shows the marks of 60 students in a science exam. How many students failed the test given that the pass mark was 30?

Marks0–910–1920–2930–3940–4950–Total
Frequency31810815660

Q8:

The table shows the marks that a class of students received in their mathematics test. How many students are in the class?

Marks0–12–34–56–78–
Frequencies845210

Q9:

Complete the frequency table which shows the marks a group of students received in a test.

Marks20–2425–2930–3435–3940–4445–4950–Total
Frequency4515910450

Q10:

The tally chart shows the marks students received in a mathematics test. How many students received less than 10 marks?

Mark5–910–1415–1920–2425–29
Frequency

Q11:

The table shows the number of days each student has been absent. Use this data to complete the frequency table.

6405422264
1326630161
4504613631
1526351660
Number of Days Absent0123456
Frequency
  • A4,7,5,5,5,4,10
  • B5,7,5,5,5,4,10
  • C5,7,5,6,5,4,10
  • D4,8,5,5,5,3,10
  • E4,7,4,5,4,4,10

Q12:

Using the data given for number of absences, complete the frequency table.

710785127
62432856
589821109
1091039778
Number of Absences1-23-45-67-88–10
Frequency
  • A3,6,5,8,10
  • B6,3,5,10,8
  • C8,10,5,3,6
  • D10,8,5,3,6

Q13:

The table of numbers shows the marks of 30 students in a mathematics exam.

25373139262327312033
35372337213324273627
32263037253132212832

Using this data, complete the frequency table.

Marks20–2324–2728–3132–3536–Total
Frequency30
  • A4, 7, 4, 3, 5
  • B5, 8, 5, 6, 6
  • C6, 8, 7, 4, 5
  • D6, 9, 8, 7, 6
  • E3, 7, 5, 8, 7

Q14:

The table of data shows the heights in centimeters of teachers at a school. Using a frequency table, find the number of teachers who are 175 cm or more.

179169193171163186178173
167166195156163190171195
156186187159172169184195
159168179155178162174167
193177159179162189163182
181167189173187159170186

Q15:

The table shows the number of days taken off work by 40 workers in a year. By constructing a frequency table or otherwise, calculate the number of workers who took 20 or more days off work.

16185201526121785
5122630232221302521
27151228111226121323
629285201210242314

Q16:

The table shows the weekly wages of 30 workers in a factory. By forming the frequency table using the intervals 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–99, find which interval has the highest frequency.

434743995447531004697
50413672383780467474
30343297903568877830
  • A60–69
  • B50–59
  • C40–49
  • D30–39

Q17:

The table shows the marks that a class of students received in a mathematics test. How many students got less than 45 marks?

Marks20–2425–2930–3435–3940–4445–4950–5455–Total
Number of Students7825659244

Q18:

Complete the frequency table by finding the value of 𝑥.

Sets10-1920-2930-3940-49𝑥-5960-69Total
Frequency3136811950

Q19:

The table shows the marks of 100 students in a recent science exam. What percentage of students received 20 marks or more?

Mark0– 10– 20– 30– 40– 50– Total
Frequency52521161914100

Q20:

Given an interval with lower limit 16 and center 23, find the upper limit of the interval.

Q21:

The table shows donations made by students to a charity. How many students donated between 60–70 pounds?

Donation in Pounds20–2930–3940–4950–5960–6970–Total Number of Students
Number of Students423716537

Q22:

The table shows the distribution of exam marks in science for 1‎ ‎000 students. By drawing a cumulative frequency curve, determine the number of students who scored 54 marks or more.

Scores20–2930–3940–4950–5960–6970–7980–8990–99Total
Frequency1051341241301191561101221‎ ‎000
  • A637 students
  • B585 students
  • C631 students
  • D124 students
  • E507 students

Q23:

The table shows the bonuses received by 75 factory workers. How many workers received a bonus which was less than 50 LE?

Bonus (LE)20–2930–3940–4950–5960–6970–Total
Number of Workers1051015251075

Q24:

The scores that 30 students achieved in a maths exam are shown in the table. By constructing a frequency table of the scores, with groups 20–23, 24–27, 28–31, 32–35, and 36–39, find the group with the lowest frequency.

28303937362828353325
39392720393136282035
32373830312529283936
  • A32–35
  • B20–23
  • C24–27
  • D28–31
  • E36–39

Q25:

The table shows the marks of 100 students in a recent mathematics exam. What percentage of students received 30 marks or more?

Marks0–910–1920–2930–3940–4950–59Total
Frequency82215221617100

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